1. Field of the Disclosure
The present invention relates generally to cognitive radios, and more particularly to spectrum-sensing cognitive radios.
2. Description of the Related Art
It has been proposed in Z. Tian and G. B. Giannakis, “A Wavelet Approach to Wideband Spectrum Sensing for Cognitive Radios,” in 2006 1st International Conference on Cognitive Radio Oriented Wireless Networks and Communications, 2006, pp. 1-5, herein incorporated by reference in its entirety, that spectrum sensing for cognitive radio wireless communications can be improved by using wavelet transforms to detect discontinuities in a power spectral density (PSD). When considering a wide band of interest without prior knowledge of how the wide band has been sub-divided into frequency bands for allocated primary users, the first task of a cognitive radio user is to discover the boundaries and extent of each subband. Only then can the cognitive radio user begin to answer the question whether the individual subbands our being used by the primary users or if the subbands are available to an opportunistic cognitive radio user. Using dormant subbands allocated to primary users provides an efficient solution to the challenge of bandwidth scarcity.
Modernly, spectrum for wireless communication is becoming scarce as demand continues increasing. Cognitive radio is seen as an excellent solution to the problem of spectrum scarcity by efficient utilization of the radio spectrum. Cognitive radio achieves this by making wireless nodes aware of their environment. The wireless nodes then modify parameters in real-time, based on predicted availability of allocated frequency bands. The most important operations of a cognitive radio is first sensing the targeted spectrum, and then deciding on the availability of spectrum in order that secondary users can benefit from unused spectrum. Spectrum sensing for cognitive radio is a very challenging task. It requires both accuracy and efficiency in order for a cognitive radio system to work effectively.
Traditional wireless systems operate under the policy of static spectrum allocation. Once a wireless service provider gets a license for using a certain band from the commercially available spectrum for a particular geographic location, he and only himself has the right to operate in that frequency band no matter whether he wants to use it 100% of the time or only 10% of the time. Any unlicensed user is prohibited to benefit from the licensed frequency band. As the trend of wireless services is shifting from voice-only to multimedia services, e.g., mobile TV, the service providers are demanding higher and higher bandwidths. Realizing the fact that the spectrum band is a limited resource, society is at the verge of spectrum unavailability for new wireless systems. In addition to this problem, a more disappointing note published in a FCC survey report pointed out that the spectrum utilization in the 0-6 GHz band varies from 15% to 85%, meaning that the actual licensed spectrum is mostly underutilized in vast temporal and geographical dimensions, as discussed in FCC, “Spectrum Policy Task Force Report,” ET Docket, 2002, herein incorporated by reference in its entirety. Hence, this inefficient utilization of licensed spectrum can be thought of as the outcome of wasteful static spectrum allocation. In order to solve the problems of spectrum scarcity and inefficient utilization, both researchers and policy makers got attracted to the recently introduced concept of cognitive radio, which was originally discussed in J. Mitola and G. Q. Maguire, “Cognitive radio: making software radios more personal,” IEEE Personal Communications, vol. 6, no. 4, pp. 13-18, 1999, herein incorporated by reference in its entirety. Recently, the IEEE 802.22 cognitive radio wireless regional area network (WRAN) standard was introduced as the first effort towards the practical use of cognitive radio, as discussed in C. Stevenson, G. Chouinard, S. Shellhammer, and W. Caldwell, “IEEE 802.22: The first cognitive radio wireless regional area network standard,” IEEE Communications Magazine, vol. 47, no. 1, pp. 130-138, January 2009, herein incorporated by reference in its entirety.
Cognitive radio is an intelligent wireless communication system that is aware of its surrounding environment (i.e., outside world), and uses the methodology of understanding-by-building to learn from the environment and adapt its internal states to statistical variations in the incoming RF stimuli by making corresponding changes in certain operating parameters (e.g., transmit-power, carrier-frequency, and modulation strategy) in real-time, with two primary objectives in mind: 1) highly reliable communications whenever and wherever needed; 2) efficient utilization of the radio spectrum. In effect, the whole operation of a cognitive radio can be represented graphically as a cycle, the so called cognitive cycle, as show in FIG. 17.
The concept of a cognitive radio (CR) network has been efficiently explained in S. Haykin, “Cognitive radio: brain-empowered wireless communications,” IEEE Journal on Selected Areas in Communications, vol. 23, no. 2, pp. 201-220, February 2005, incorporated herein by reference in its entirety, and in I. F. Akyildiz, W.-Y. Lee, M. C. Vuran, and S. Mohanty, “NeXt generation/dynamic spectrum access/cognitive radio wireless networks: A survey,” Computer Networks, vol. 50, no. 13, pp. 2127-2159, September 2006, incorporated herein by reference in its entirety. This intelligent radio has the cognitive capability to sense its surrounding environment, and to determine appropriate operating parameters for it in order to adapt to the dynamic radio environment, all in real-time. The fundamental role of a CR is to acquire the best available spectrum for its users, based on its cognitive capability and re-configurability. Since most of the commercially available spectrum is already allocated, the real challenge is to share seamlessly the unused spectrum of the PU. Consider an example model of spectrum usage across time and frequency displayed in FIG. 1.
The interference-based detection method calculates the maximum amount of interference that the primary receiver could tolerate. As long as the cumulative RF energy from multiple sources, including the secondary users, is below under a certain limit, the secondary users are allowed to transmit in a specific spectrum band. One model to measure the interference at the receiver was introduced by FCC in FCC, “ET Docket No 03-237 Notice of inquiry and notice of proposed Rulemaking,” 2003, herein incorporated in its entirety by reference, referred to as the interference temperature model. Using this model, a radio receiver can be designed to operate over a range at which the received interference level is below the interference temperature limit. The limitations of this model are that it needs information about the unlicensed user's signal modulation, activity patterns of the primary and secondary users, in addition to having control over the power levels of the SU as discussed in T. X. Brown, “An analysis of unlicensed device operation in licensed broadcast service bands,” in First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, 2005. DySPAN 2005, pp. 11-29, herein incorporated in its entirety by reference. Also the cognitive user may not be aware of the exact location of the primary receivers, which makes it impossible to measure the influence of the cognitive user's transmission on all the potential primary receivers. Because of the inherent complexities in the receiver's interference detection method, the method has gained less attention as compared to the transmitter detection methods for cognitive radios.
Transmitter detection techniques have attracted most attention because of their simplicity. When this technique is used, the cognitive radio focuses on the local observation of the signal from a primary user (transmitter). Transmitter detection can be performed either with one cognitive radio or by a group of cognitive radios cooperatively sensing a targeted spectrum band. The latter case is sometimes referred to as collaborative (cooperative) detection as discussed in A. Ghasemi and E. S. Sousa, “Collaborative spectrum sensing for opportunistic access in fading environments,” in First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, 2005. DySPAN 2005, pp. 131-136, herein incorporated in its entirety by reference. These (transmitter detection) techniques can be further divided into Blind/Semi-Blind Spectrum Sensing and Non-Blind Spectrum Sensing as discussed in R. Umar and A. U. H. Sheikh, “A comparative study of spectrum awareness techniques for cognitive radio oriented wireless networks,” Physical Communication, August 2012, herein incorporated in its entirety by reference. The key difference among these schemes lies in the amount of a priori knowledge about the Primary User (PU) signal that is required by the cognitive radio to perform spectrum sensing. The former approach (Blind/Semi-Blind SS) is usually used when the CR have no prior information about the characteristics of the primary user signal, channel, and the noise power. The best possible knowledge the CR can have is the estimate of noise variance, hence the term Semi-Blind SS. Energy detection as discussed in A. Sahai and N. Hoven, “Some fundamental limits on cognitive radio,” Allerton Conference on Comm., Control and Computing, 2004, herein incorporated in its entirety by reference, and discussed in H. Urkowitz, “Energy detection of unknown deterministic signals,” Proceedings of the IEEE, vol. 55, no. 4, pp. 523-531, 1967, herein incorporated in its entirety by reference, and statistical-analysis-based detection falls under the category of Blind/Semi-Blind SS. When prior information is not available or cannot be extracted by the CR, Energy Detector is the best and simplest option to perform sensing. Energy detection is the least demanding approach as it makes the receiver implementation task relatively simple. Under the category of Non-Blind Spectrum Sensing, we have the following techniques: 1) Matched Filter detection, and 2) Cyclostationary feature detection, as discussed in A. Ghasemi and E. S. Sousa, “Spectrum sensing in cognitive radio networks: requirements, challenges and design trade-offs,” IEEE Communications Magazine, vol. 46, no. 4, pp. 32-39, April 2008, herein incorporated in its entirety by reference. Matched filter detection and cyclostationary feature detection techniques require a priori knowledge about the PU signal.
A cyclostationary feature detector is robust to noise power uncertainty. The cyclostationary feature detector can also differentiate between a PU signal and other CR users' signal provided that all the signals exhibit different cyclic features, which is usually the case. However, the complexity of the cyclic feature detector comes from the facts that it requires the knowledge of different signal's modulation formats, as well as requires long observation times. These complexities make the feature detector implementation less favorable as compared to energy detector.
Wavelet based sensing falls under the category of Energy Detection. The relationship among all of these approaches is summarized by the branch diagram shown in FIG. 18. Wavelets are simply a set of basis functions. A wavelet is effectively a limited-duration waveform that has an average value of zero. The wavelet transform (WT) is a mathematical tool used for projecting signals, similar to other tools that are used for signal analysis, e.g., fourier transform (FT). A comparison of Fourier transform and wavelet transform basis functions is shown in FIG. 19. Fourier analysis is perhaps the most well-known transformation to date, which transforms a time-domain signal into the frequency-amplitude representation of the signal. The FT provides the global information on frequencies presented in the signal regardless of the exact time they appear in the signal. When looking at a Fourier transform of a signal, it is impossible to tell when a particular event has happened. This property, on one hand, does not negatively affect the suitability of FT to stationary signals, but, on the other hand, makes the FT unsuitable when the signal being analyzed is non-stationary. For analyzing non-stationary signals, a transformation technique that can provide time-frequency information is necessary. Instead of the traditional FT transformation, we focus here on the WT. While the FT provides information only about the frequency components contained in a signal, the WT provides both time and frequency or time and scale representation of a signal under analysis.
The bases of the FT are time-unlimited sinusoidal waves; they extend from −∞ to +∞. Also sine waves are predictable and smooth, as compared to wavelet functions which tend to be rough and anti-symmetric.
While the FT is a process of decomposing a signal into sine waves of different frequencies, the WT decomposes the signal into shifted and scaled versions of the original (or mother) wavelet. Since a wavelet is an irregular (or anti-symmetric) wave, it is better suited for analyzing signals with local singularities (or sharp edges) than the more regular sinusoids.
A wavelet is represented by a mathematical function that divides a given function or continuous-time signal into different frequency components. A wavelet is generated from a single mathematical function called a mother wavelet (as shown in FIG. 3 for Gaussian wavelets), which is a finite-length or fast-decaying oscillating waveform both in time and in frequency. Mother wavelets also include some special properties such as their integer translations and dyadic dilations, which form an orthogonal basis for the energy-limited signal space. Daughter wavelets are scaled and translated (t) copies of the mother wavelet. WTs have advantages over traditional FTs for representing functions that have discontinuities and sharp changes (as inherent in user data). Moreover, wavelet transforms provide a means for accurately deconstructing and reconstructing finite, non-periodic and/or non-stationary signals, which FTs usually cannot do.
The Continuous Wavelet Transform (CWT) of a signal, s(t), is defined as the sum over all times of the signal multiplied by scaled and shifted versions of a mother wavelet function ψ(t). Mathematically, the CWT of a finite energy signal, s(t), is defined as:
            C      ⁡              (                  a          ,          b                )              -                  ∫        R            ⁢                        s          ⁡                      (            t            )                          ⁢                  1                      a                          ⁢                  ψ          ⁡                      (                                          t                -                b                            a                        )                          ⁢                  ⅆ          t                      ,      a    ∈          R      +        ,      b    ∈    R    ,      s    ∈                  L        2            ⁡              (        R        )            where C(a, b) are the continuous wavelet transform coefficients and a is a positive scaling parameter, and b denotes the amount of time-shift, as discussed in I. Daubechies, Ten Lectures on Wavelets, 1st ed. SIAM, 1992 as, herein incorporated in its entirety by reference. The result of this transformation is a scale-position or scale-time representation C(scale, tame). The inverse CWT can be used to recover the original signal s(t).To recover the original signal from its CWT coefficients, the Inverse Continuous Wavelet Transform is used, and is defined by:
            s      ⁡              (        t        )              =                  1                  K          ψ                    ⁢                        ∫                      R            +                          ⁢                              ∫            R                    ⁢                                    C              ⁡                              (                                  a                  ,                  b                                )                                      ⁢                          1                              a                                      ⁢                          ψ              ⁡                              (                                                      t                    -                    b                                    a                                )                                      ⁢                                          da                ⁢                                                                  ⁢                db                                            a                2                                                          ,where Kψ is a constant depending on ψ.
It is important to understand the difference between the CWT and its discrete counter-part, the Discrete Wavelet Transform (DWT). The CWT can operate at any arbitrary scale. We can control the range of scales at which we would like to compute wavelet coefficients. The scales can range from one up to some maximum value determined depending on the level of details needed and the application of interest. In contrast with the CWT, the Discrete Wavelet Transform (DWT) calculates wavelet coefficients at specific set of scales. When the scales and positions are expressed as powers of two, we call these dyadic scales and dyadic positions. In this way, DWT is less computationally expensive than the CWT, yet as accurate. Mathematically, it can be defined after discretizing Equation 0 by limiting a and b to a discrete lattice (a=2j, b=k2j, (j,k)εZ2):C(j,k)∫Rs(t)ψj,k(t)dt,(j,k)εZ2,sεL2(R)where C(j, k) are the discrete wavelet transform coefficients. ψj,k(t) are the wavelet basis functions or wavelet expansion functions, which are related to the original mother wavelet function ψ(t) as follows:ψj,k(t)=2−j/2ψ(2−jt−k)where j and k are the dilation and translation parameters, respectively.To reconstruct the original signal, the Inverse Discrete Wavelet Transform (IDWT) is given by:
      s    ⁡          (      t      )        =            ∑              j        ∈        z              ⁢                  ∑                  k          ∈          z                    ⁢                        C          ⁡                      (                          j              ,              k                        )                          ⁢                                            ψ                              j                ,                k                                      ⁡                          (              t              )                                .                    
An efficient scheme for implementing the wavelet transform using filters was introduced in S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 674-693, July 1989, herein incorporated in its entirety by reference, and is classically known as a two-channel subband coder as discussed in G. Strang and T. Nguyen, Wavelets and Filter Banks, 2nd ed. Wellesley College, 1996, p. 520, herein incorporated in its entirety by reference. This method provides a fast implementation of the wavelet transform. The wavelet decomposition is composed of low-pass and high-pass filters. The signal of interest is fed into both of these filters. The output of the filters is followed by dyadic decimation. Finally, the resulting coefficients are called approximations and details, respectively. The approximation coefficients (that correspond to the low-pass filter) are the high-scale, low-frequency components of the input signal, whereas the detail coefficients (that correspond to the high-pass filter) are the low-scale high-frequency components of the input signal. The wavelet decomposition at the first step is illustrated in FIG. 20.
In FIG. 20, the input signal s is fed into the two complementary filters and the outputs are the approximation coefficients, cA1, and the detail coefficients, cA2. The wavelet decomposition can be continued iteratively where at each level of decomposition; the approximations are decomposed into the next level's approximation and detail coefficients. This process leads to the analysis of the signal by decomposing it into several low resolution components and can be represented as the wavelet decomposition tree shown in FIG. 21.
As mentioned before, non-stationary signals can be best dealt with the wavelet transform. In addition to that, an attractive property of the WT is its ability to perform local analysis of a larger signal, and to detect singularities (discontinuities) in the signal. This property of WT can be used in edge detection as discussed in S. Mallat and S. Zhong, “Characterization of signals from multiscale edges,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 7, pp. 710-732, July 1992, herein incorporated in its entirety by reference.
The primary users (PUs) (11, 12, 13, 14, and 15 in FIG. 1) are only active within certain time intervals. The no-activity gaps between active intervals are referred to as spectrum holes. If such spectrum holes can be detected efficiently, then these can be used by a secondary user or cognitive radio user (CR) 10 resulting in better spectrum utilization. For example in FIG. 1, at time t=0, CR 10 is using the frequency band allocated to PU 11. During the opportunistic spectrum access, wherein the CR 10 uses the spectrum allocated to PU 11, the CR 10 must monitory when PU 11 restarts using the allocated spectrum, at which time CR 10 must either move to another spectrum hole, or change operating parameters, e.g., modulation scheme, in order to avoid interference with the primary transmission. If neither of the previous two choices are available CR 10 must stop transmitting until CR 10 can transmit without interfering with the signal of a PU. In FIG. 1, the spectrum hole becomes available at the spectrum allocated to PU 14 and CR 10 changes frequency to utilize this spectrum hole while it is not used by a PU. When PU 14 begins transmitting again, CR 10 changes frequency the frequency band allocated to PU 12 while it is not being used by a PU.
The Cognitive Cycle steps are: 1) Spectrum Sensing: A CR examines the targeted frequency band(s), extracts relevant information, and identifies possible spectrum holes; 2) Spectrum Analysis: The detected spectrum holes are characterized and channel conditions are estimated within each hole; and 3) Spectrum Decision: Based on the cognitive user requirements, e.g., data rate and required bandwidth, the cognitive radio determines the best available spectrum hole for the cognitive user transmission.
While the cognitive user is transmitting over a frequency band allocated to a PU, it is important to keep track of the changes in the radio environment. For example, when the current channel conditions become worse or when the licensed user reappears, the operation of spectrum mobility comes into play, as shown in FIG. 1. During this operation, the cognitive radio switches from the current channel to some other spectrum hole, a phenomenon referred to as spectrum handoff.
From the previous discussion, it is clear that a necessary task prior to dynamic spectrum access is spectrum sensing. It is the first phase in the cognitive cycle. In this phase, efficient spectrum sensing techniques are used to track the radio environment which may change in time and space. Several spectrum sensing methods have been discussed in the literature with their merits and demerits. See, e.g., R. Umar and A. U. H. Sheikh, “A comparative study of spectrum awareness techniques for cognitive radio oriented wireless networks,” Physical Communication, August 2012, incorporated herein in its entirety, and T. Yucek and H. Arslan, “A survey of spectrum sensing algorithms for cognitive radio applications,” IEEE Communications Surveys & Tutorials, vol. 11, no. 1, pp. 116-130, 2009, incorporated herein in its entirety. Spectrum sensing techniques can be classified into two main categories, namely, transmitter detection, and interference-based detection. Wavelet based sensing fall under the category of Energy Detection.
When the targeted frequency band is narrowband, the radio system front end can be implemented using tunable narrowband Band-Pass Filters (BPF). However, when the spectrum utilization is high, one needs to sense a wideband spectrum in order to detect efficiently spectrum whitespaces. Under this scenario, it is inefficient to install multiple narrowband BPFs at the radio front-end to perform the sensing task. Alternatively, if only one narrowband BPF is used to scan the entire wideband (frequency range) in blocks, this becomes time consuming hence reducing the overall performance of the cognitive radio.
Observing the fact that a wideband spectrum can be thought of as a sequence of consecutive subbands, where the Power Spectral Density (PSD) within each subband is almost flat and some discontinuities exist at the boundaries of subbands. These discontinuities in the wideband PSD carry key information about the location of boundaries and the potential spectrum holes. A powerful mathematical tool for analyzing signal's local singularities is the Wavelet Transform, which can be used to extract information about edges in the signal spectrum as explained in S. Mallat and W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Transactions on Information Theory, vol. 38, no. 2, pp. 617-643, March 1992, incorporated herein by reference in its entirety. In our case, edges in the wideband PSD refer to the boundaries of two consecutive subbands of different power levels within the wideband of interest. After the identification of subbands, energy is estimated for each of these, which carries important information on spectrum holes available for opportunistic sharing. This idea of using Wavelet Transform on the received wideband signal's PSD was first proposed in Z. Tian and G. B. Giannakis, “A Wavelet Approach to Wideband Spectrum Sensing for Cognitive Radios,” in 2006 1st International Conference on Cognitive Radio Oriented Wireless Networks and Communications, 2006, pp. 1-5, incorporated herein by reference in its entirety.
As shown in FIG. 2, wireless signals from the licensed users shall exist within a wide band of interest in assigned non-overlapping frequency bands with possibly non-similar powers. In the wide band of interest, there are discontinuities in the PSD at the edges of the assigned frequency bands. A cognitive user, without prior knowledge of the number, bandwidth, or locations of the assigned frequency bands, can identify the frequency band edges by convolving together the PSD and wavelet functions in the frequency domain.
In FIG. 2, the radio signal received at the CR has N frequency bands in the interval [f0,fN] being sensed by the cognitive user. The cognitive user must first identify the frequency bands assigned to primary users by identifying discontinuities in the PSD at frequencies f1<f2< . . . <fN−1. Next the cognitive user defines each subband such that the nth subband is given by Bn=[fn−1,fn]. The PSD as a function of frequency is given by Sr(f). After identifying the subband frequency intervals, {fn}n=1N−1, the PSD level within each subband is averaged to obtain βn.
The wavelet smoothing function is given by φ(f), and FIG. 3 shows a non-limiting example of φ(f) using a to be a Gaussian wavelet. The dilation of the wavelet smoothing function φ(f) by a scale factor s is given by:
            φ      s        ⁡          (      f      )        =            1      s        ⁢          φ      ⁡              (                  f          s                )            The CWT of Sr(f) is defined as the convolution of the observed signal PSD with the wavelet function:WsSr(f)=Sr*φs(f).WsSr(f) provides information on the local structure of Sr(f), such that taking the derivative of WsSr(f) and looking for the extrema will give the largest averaged discontinuities in the PSD. This operation is expressed mathematically as:
            W      s      ′        ⁢                  S        r            ⁡              (        f        )              =      s    ⁢                  ⅆ                                              ⅆ        f              ⁢          (                        S          r                *                  φ          s                    )        ⁢                  (        f        )            .      So, the local modulus maxima Ws′Sr(f) represent the edges in the PSD Sr(f). More formally, the identification of frequency boundaries {fn}n=1N−1 can be expressed as:{circumflex over (f)}n=maximaf{|Ws′Sr(f)|},fε[f0,fN].Dyadic scales will be used (i.e., s=2j, j=1, 2, . . . , J.) as a non-limiting example of scale factors.
FIG. 3 shows an example of a wavelet smoothing function. FIG. 4 shows a flow chart for the basic wavelet transform method 310 for determining boundaries between frequency bands. As discussed above the method includes a first step of acquiring a time domain signal 311. The second step is estimating the power spectral density (PSD) 312. The third step is calculating the wavelet coefficients 313, and the final step is solving for discontinuities in the PSD 314.
The above basic method can be improved by taking advantage of the unique information provided by different dyadic scales. Small dyadic scales can resolve narrow band features but are susceptible to misidentifying high frequency noise as the edge of a frequency band. In contrast, large dyadic scales are not susceptible to high frequency noise but also smooth out narrow band features. Taking the product of CWT of Sr(f) for multiple dyadic scales suppresses the noise-induced spurious local maxima, which are random at each scale. This multi-scale product is defined as:
            U      J        ⁢                  S        r            ⁡              (        f        )              =            ∏              j        =        1            J        ⁢                  ⁢                  W                  s          =                      2            j                          ′            ⁢                                    S            r                    ⁡                      (            f            )                          .            
The method provides the estimation of frequency edges {fn} of interest, by picking the maxima of the multi-scale product in 0. The noise-induced spurious local maxima of |Ws′Sr(f)| are random at every scale and tend not to propagate though all J scales; hence, they do not show up as the local maxima of |UJSr(f)| and peaks are enhanced due to edges while noise is suppressed:{circumflex over (f)}n=maximaf{|UJSr(f)|},fε[f0,fN].
FIG. 4 shows a flow chart for the multi-scale-product method 320 of determining boundaries of frequency bands allocated to PU using wavelet transform coefficients. As discussed above the method includes a first step of acquiring a time domain signal 311, a second step of estimating the power spectral density (PSD) 312, a third step of calculating the wavelet coefficients 313, a fourth step of calculating the multi-scale product 321, and final step of solving for discontinuities in the PSD 314.
After determining the frequency bands allocated to PU, the next step is to measure the energy in each frequency band and decided whether it is being used or if it is available for use by the CR. FIG. 6 depicts a simple block diagram of an energy detector for determining if a frequency band is being used. The observed signal x(t) is fed to a band-pass filter which limits the bandwidth to W and selects some center frequency fc. Following the BPF, squaring device and an integrator of a certain observation interval, T, are used. Finally, the measured energy from the integrator is compared to a pre-threshold, λ, and a decision about the presence or the absence of the primary user is made. The value of the threshold λ depends mainly upon the noise variance.
Instead of frequency-domain analysis, one can consider the problem of spectrum sensing in time domain. One of the most common techniques used in time domain is Energy Detection. As mentioned before, when a cognitive radio receiver does not have any prior knowledge on the primary user's signal and the only thing that is known is the power of the random Gaussian noise, then the optimal solution in terms of implementation is an Energy Detector (ED) as discussed in A. Sahai and N. Hoven, “Some fundamental limits on cognitive radio,” Allerton Conference on Comm., Control and Computing., 2004, herein incorporated in its entirety by reference. The idea of determining the presence of unknown deterministic signals using Energy Detector was first discussed in H. Urkowitz, “Energy detection of unknown deterministic signals,” Proceedings of the IEEE, vol. 55, no. 4, pp. 523-531, 1967, herein incorporated in its entirety by reference. FIG. 6 depicts a simple block diagram of an energy detector.
The observed signal x(t) is fed to a band-pass filter which limits the bandwidth to W and selects some center frequency fc. Following the BPF, squaring device and an integrator of a certain observation interval, T, are used. Finally, the measured energy from the integrator is compared to a pre-threshold, λ, and a decision about the presence or the absence of the primary user is made. The value of the threshold λ depends mainly upon the noise variance.
The input signal x(t) can have several possible forms based on whether the primary user is present or absent, which we denote by hypotheses H1, and H0, respectively:
      x    ⁡          (      t      )        =      {                                                                      n                ⁡                                  (                  t                  )                                            ,                                                          H              0                                                                                                            h                  ×                                      s                    ⁡                                          (                      t                      )                                                                      +                                  n                  ⁡                                      (                    t                    )                                                              ,                                                          H              1                                          ,      where s(t) represents the primary user's signal, h is the channel gain, and n(t) is the noise.
In FIG. 6, the output of the integrator is effectively the decision statistic, which is represent by Y. In order to analyze the performance of the above mentioned energy detector, the statistical distribution of Y has to be known under both hypotheses. The decision statistic Y will have the following distributions:
  Y  ~      {                                                      χ                              2                ⁢                TW                            2                        ,                                                H            0                                                                                          χ                                  2                  ⁢                  TW                                2                            ⁡                              (                                  2                  ⁢                  γ                                )                                      ,                                                H            1                              where χ2TW2 denotes a central chi-square distribution and χ2TW2 (2γ) denotes a non-central chi-square distribution, both with the same degrees of freedom, i.e., 2TW (TW is the time-bandwidth product). The non-central chi-square distribution has a non-centrality parameter of 2γ, where γ is the receiver SNR (cognitive radio). For simplicity, we denote the time-bandwidth product as u=TW, and assume that T and W are chosen such that u has an integer value.
FIG. 7 depicts the two regions, H0 and H1, separated by a single threshold λ. This threshold divides the decision as either present if the observed energy is above the threshold (hypothesis H1 is true), or otherwise absent (hypothesis H0 is true). The performance of the energy-detector based spectrum sensing is established mainly on two parameters, namely, probability of misdetection Pm and probability of false alarm Pf. If the cognitive user (CR) decides an absence while the primary user (PU) is present; this error is represented with the probability of misdetection Pm, which would cause a substantial interference at the PU. On the other hand, if the CR decides a presence while the PU is absent, the cognitive user would miss a spectrum usage opportunity; a phenomenon represented by the probability of false alarm Pf. Jointly, the probability of misdetection Pm and the probability of false alarm Pf define what is called Complementary Receiver Operating Characteristics (C-ROC). Sometimes instead of Pm, we use the probability of detection Pd which is related to Pm as 1−Pm. Probability of detection Pd defines the probability with which the CR will detect the presence of PU, given the PU is actually active. These parameters can generally be evaluated as:Pm=Pr(Y<λ|H1)Pf=Pr(Y>λ|H0)Pd=1−Pm=Pr(Y>λ|H1)where, as before, λλ is the decision threshold. The plot of Pd vs. Pf is called Receiver Operating Characteristics (ROC).
There is always a trade-off between Pd (or Pm) and Pf. As illustrated in FIG. 22, we can have two distinct PDFs of a received signal, corresponding to two possible hypotheses, H0 and H1. By varying the threshold, we can control the two type errors, namely, Pm and Pf. If the threshold is kept excessively low, Pm decreases at the expense of increased Pf. A high Pf implies spectrum inefficient utilization because of high false alarms. Alternatively, if the threshold is set needlessly high, we can reduce Pf at the cost of increasing Pm. A high Pm implies a high probability of interfering while PU is active. Evidently, we cannot reduce both types of error simultaneously. The optimal approach is to use Neyman-Pearson detector as discussed in S. M. Kay, Fundamental of Statistical Signal Processing: Detection Theory. Englewood Cliffs, N.J.: Prentice-Hall, 1998, herein incorporated in its entirety by reference, where we constrain Pf to a fixed value, and minimize Pm. In other words, we fix the value of Pf, and try to maximize Pd.
If we consider no fading, then h will be a constant in equation 0. For such additive white Gaussian noise (AWGN) environment, the closed-form expressions for Pd and Pf has been reported in F. F. Digham, M. S. Alouini, and M. K. Simon, “On the energy detection of unknown signals over fading channels,” in IEEE International Conference on Communications, 2003. ICC '03, 2003, vol. 5, pp. 3575-3579, herein incorporated by reference in its entirety, as:PdAWGN=Qu(√{square root over (2γ)},√{square root over (λ)})where Qu(a, b) is the generalized Marcum Q-function as discussed in A. Nuttall, “Some integrals involving the Q_M function (Corresp.),” IEEE Transactions on Information Theory, vol. 21, no. 1, pp. 95-96, January 1975, herein incorporated by reference in its entirety, and
      P    f    =            Γ      ⁡              (                  u          ,                      λ            2                          )                    Γ      ⁡              (        u        )            where Γ(.,.) and Γ(.) are the incomplete and complete gamma function, respectively.
For the case where we assume the channel fading h to be Rayleigh distributed, only the expression for Pd will change. Under Rayleigh fading, the signal-to-noise-ratio (SNR) γ will follow exponential distribution and for this case Pd Ray is shown to be derived as:
      P    dRay    =                    ⅇ                  -                      λ            2                              ⁢                        ∑                      n            =            0                                u            -            2                          ⁢                              1                          n              !                                ⁢                                    (                              λ                2                            )                        n                                +                            (                                    1              +                              γ                _                                                    γ              _                                )                          u          -          1                    ⁡              [                              ⅇ                          -                              λ                                  2                  ⁢                                      (                                          1                      +                                              γ                        _                                                              )                                                                                -                                    ⅇ                              -                                  λ                  2                                                      ⁢                                          ∑                                  n                  =                  0                                                  u                  -                  2                                            ⁢                                                1                                      n                    !                                                  ⁢                                                      λ                    ⁢                                                                                  ⁢                                          γ                      _                                                                            2                    ⁢                                          (                                              1                        +                                                  γ                          _                                                                    )                                                                                                          ]            where γ is the average received SNR. Since Pf is considered when there is no signal present and as such is independent of SNR γ, therefore, its expression remains the for the cases of fading and non-fading channels.
A high Pf implies spectrum inefficient utilization because of high false alarms. Alternatively, if the threshold is set needlessly high, we can reduce Pf at the cost of increasing Pm. A high Pm implies a high probability of interfering while PU is active. Evidently, we cannot reduce both types of error simultaneously. The optimal approach is to use Neyman-Pearson detector as discussed in S. M. Kay, Fundamental of Statistical Signal Processing: Detection Theory. Englewood Cliffs, N.J.: Prentice-Hall, 1998, herein incorporated by reference in its entirety, where we constrain Pf to a fixed value, and minimize Pm. In other words, we fix the value of Pf, and try to maximize Pd.
As with any wireless communication system, the performance degrades in multipath fading channels. One way to overcome the effects of multipath fading is to use multiple antennas to improve performance as discussed in S. M. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE Journal on Selected Areas in Communications, vol. 16, no. 8, pp. 1451-1458, 1998, herein incorporated in its entirety by reference. Similarly, fading in wireless channels creates uncertainty in the SNR at the CR receiver input, making it difficult for the CR to provide a reliable decision about the absence or presence of the PU, since when the CR is experiencing a deep fading or shadowing due to large obstacles over the primary-to-secondary channel, the amount of energy observed during a fixed time-bandwidth product may not be enough to decide about the presence of a PU. One way to overcome this problem is to increase the amount of local processing which, in the case of energy detector, translates into increasing the time-bandwidth product. However, this is not always possible due to constraints of the sensing period set by the regulator.
Rather than increasing the time-bandwidth product, the cognitive user can cooperate with neighboring cognitive users as discussed in G. Ganesan, Y. Li, and S. Li, “Spatiotemporal Sensing in Cognitive Radio Networks,” in 2007 IEEE 18th International Symposium on Personal, Indoor and Mobile Radio Communications, 2007, pp. 1-5, herein incorporated in its entirety by reference. Since the multipath fading statistics fluctuates considerably on the scale of a fraction of wavelength and shadowing fluctuates considerably on the scale of 20-500 m based on the nature of environment, it is highly unlikely that multiple cooperating CRs will experience deep fade and/or large obstacles at the same time as discussed in J. Ma, G. Y. Li, and B. H. Juang, “Signal processing in cognitive radio,” Proceedings of the IEEE, vol. 97, no. 5, pp. 805-823, 2009, herein incorporated in its entirety by reference, F. F. Digham, M.-S. Alouini, and M. K. Simon, “On the Energy Detection of Unknown Signals Over Fading Channels,” IEEE Transactions on Communications, vol. 55, no. 1, pp. 21-24, January 2007, herein incorporated in its entirety by reference, and I. F. Akyildiz, B. F. Lo, and R. Balakrishnan, “Cooperative spectrum sensing in cognitive radio networks: A survey,” Physical Communication, vol. 4, no. 1, pp. 40-62, March 2011, herein incorporated in its entirety by reference.
The cooperation between multiple CRs can be carried in either a centralized or a distributed fashion as shown in FIG. 8 and FIG. 9. FIG. 8 shows cognitive users CR1 20, CR2 30, CR3 40, CR4 50, and CR5 60 reporting measurement results to a centralized node CR0 70 called the fusion center (FC). In contrast, FIG. 9 shows distributed network of cognitive users, where each CR operates as its own FC. In both cases the FC operates in a nearly identical manner. Thus the essentially difference between distributed and centralized network architectures is the location of the FC, not the function of the FC. For simplicity we discuss only the centralized cooperation system of CRs, but the results are equally applicable to a distributed cooperation system of CRs.
When a centralized fusion center (CR0 70 in FIG. 8) is used to handle the different cognitive decisions, the cooperative spectrum sensing can be performed in the following manner: 1) All the cooperating cognitive users start by sensing a targeted band independently; 2) Each cooperating node would forward either its local binary decision or it can just send its observation value directly to the fusion center (FC) 70 over the reporting channel 19; 3) Finally, the fusion center 70 fuses all the received data (or decisions) to infer the presence or absence of the PU 20. The fusion center 70 can also be referred to as common receiver, master node, base station, combining node, and designated controller. As shown in FIG. 8, CR0 is the FC while CR1-CR5 (20, 30, 40, 50, and 60) are the cooperating CRs. When using cooperation among multiple CRs for spectrum sensing, certain protocols need to be defined for the purpose of sharing sensing information over the reporting channel 19. In contrast to the reporting channel 19, the physical point-to-point connection between the PU and a CR for the purpose of sensing the primary transmitter's signal is called a sensing channel 18. Different architecture have been proposed for reporting channels, e.g. using ISM band and ultra wide band (UWB) have been discussed in C. Guo, T. Zhang, Z. Zeng, and C. Feng, “Investigation on Spectrum Sharing Technology Based On Cognitive Radio,” in 2006 First International Conference on Communications and Networking in China, 2006, pp. 1-5, and J. Perez-Romero, O. Salient, R. Agusti, and L. Giupponi, “A Novel On-Demand Cognitive Pilot Channel Enabling Dynamic Spectrum Allocation,” in 2007 2nd IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, 2007, pp. 46-54. A simple protocol using time division multiple access (TDMA) to share the sensing information with the fusion center is proposed in P. Pawelczak, C. Guo, R. V. Prasad, and R. Hekmat, “Clusterbased spectrum sensing architecture for opportunistic spectrum access networks,” in IEEE Vehicular Technology Conference VTC2007, 2007, where the cooperating CRs are divided into clusters based on their geographical location and send their sensing data to the particular cluster head only during the assigned time slots.
It is very important to consider that the cooperation mechanism should have as low as possible overhead, and it should be robust to network changes and failures. Also, the amount of delay needs to be minimized for a particular cooperation algorithm. Usually, such type of protocols are defined at Medium Access Layer (MAC) as discussed in L. Musavian and T. Le-Ngoc, “Cross-layer design for cognitive radios with joint AMC and ARQ under delay QoS constraint,” in 2012 8th International Wireless Communications and Mobile Computing Conference (IWCMC), 2012, pp. 419-424, herein incorporated in its entirety by reference.
Based on whether the CRs are sending their 1-bit binary decision or their observation value to the fusion center, the combination is called either decision fusion or data fusion, respectively. Sometimes the terms hard combination and soft combination are used instead of using the respective terms decision fusion or data fusion.
FIG. 10 shows a proposed cooperative spectrum sensing framework from I. F. Akyildiz, B. F. Lo, and R. Balakrishnan, “Cooperative spectrum sensing in cognitive radio networks: A survey,” Physical Communication, vol. 4, no. 1, pp. 40-62, March 2011, herein incorporated in its entirety by reference. The framework consists of the PU, cooperating CRs, FC, the RF channels (sensing and reporting channels), and an optional remotely located database. As shown in the framework, a group of collaborative CRs, presumably independent of each other, perform targeted sensing using their RF frontend 21. The processing unit, 22 of CR1 20 may include, at least, a signal processor 23, data fusion 24, and hypothesis testing 25 entities. The RF frontend 21 is capable to be configured for data transmission or local sensing. Besides that, analog-to-digital conversion will also be done by the RF frontend 21. The local observations of the cooperating CRs (20, 30, and 40) can directly be transmitted to the FC 70, or it can be locally processed to provide a decision to the FC 70. Usually, certain amount of processing on the local observations is needed to minimize the bandwidth requirement over the reporting channels. The processing may include the evaluation of the energy statistics and thresholds. When the local decision or the observations are ready, a request to a higher layer (e.g., MAC layer) is sent to acquire the access of a control channel. The FC 70 in the centralized CSS framework 100 is a powerful cooperating CR which has all the capabilities as the other CRs. In addition, the FC 70 has other functionalities, such as user selection and knowledge base, to undertake the cooperation tasks successfully. Based on the requirement and the ability of the FC 70, the FC 70 can be connected to an external (remotely located) database 81 through an ultra-high speed communication medium 82 (e.g., fiber optics). This external database will assist the FC and can provide information regarding the PU 20 activity and white spaces.
When decision-fusion is used, each CR compares its observed energy value with pre-fixed threshold λ, if the observed value is greater than λ, the reported decision is 1 (H1), while the reported decision is 0 (H0) if the value is less than the threshold. After collecting L local 1-bit decisions, the fusion center makes an occupancy-decision based on a certain decision-fusion rule, which can be represented as
  Z  =            ∑              i        =        1            L        ⁢                  D        i            ⁢              {                                                                                                  ≥                    K                                    ,                                                                              H                  1                                                                                                                          <                    K                                    ,                                                                              H                  0                                                              ,                    As discussed in K. Ben Letaief, “Cooperative Communications for Cognitive Radio Networks,” Proceedings of the IEEE, vol. 97, no. 5, pp. 878-893, May 2009, herein incorporated by reference in its entirety.
If there exists at least K out of L CRs having their local observation values above the pre-fixed thresholds, then the fusion center will infer presence of the PU, i.e., H1, otherwise the fusion center will declare that there is no PU signal transmitted, i.e, H0. Such decision criterion is also called K-out-of-L rule as discussed in P. K. Varshney, Distributed Detection and Data Fusion. New York: Springer-Verlag, 1997, p. 299, herein incorporated in its entirety by reference. It was shown in A. Ghasemi and E. S. Sousa, “Spectrum sensing in cognitive radio networks: the cooperation-processing tradeoff,” Wireless Communications and Mobile Computing, vol. 7, no. 9, pp. 1049-1060, November 2007, herein incorporated in its entirety by reference, that under the case of distributed individual and independent decisions, the optimum (in terms of detection performance) decision-fusion rule is 1-out-of-L rule (i.e., OR rule). Therefore, in the rest of the thesis we shall resort to the OR rule as our final decision-fusion rule. Instead of calculating individual thresholds for each cooperating user, for simplicity, it is assumed that all collaborative cognitive users have the same decision rule (i.e., same threshold λ), according to some fixed cooperative probability of false-alarm, Qf as discussed in A. Ghasemi and E. S. Sousa, “Collaborative spectrum sensing for opportunistic access in fading environments,” in First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, 2005. DySPAN 2005, pp. 131-136, herein incorporated in its entirety by reference.
FIG. 11 shows a flow chart of the hard decision time domain method 420 for a cooperative spectrum sensing network of CRs to determine whether a frequency band allocated to PUs is being used. The method includes a first step of calculating the energy in the frequency band 411, a second step of determining the received energy value 412, a third step of making a hard decision about whether the frequency band is used 421, a fourth step of transmitting the CR result to a FC 413, a fifth step of the FC combining results from multiple CRs to obtain a final decision 422, and a final step of transmitting the final decision to the CRs 415.
Alternatively to the decision fusion for hard decisions discussed above, the fusion center can also exploit the diversity provided by using a data-fusion criterion to determine the occupancy state of the targeted band. In data-fusion, each CR simply reports their original sensing data to the fusion center. Although, data-fusion imposes large amount of communication overhead over the control channel, but it has excellent detection performance as discussed in J. Ma, G. Y. Li, and B. H. Juang, “Signal processing in cognitive radio,” Proceedings of the IEEE, vol. 97, no. 5, pp. 805-823, 2009, herein incorporated in its entirety by reference. A data-fusion based cooperative spectrum sensing method was proposed in S. Haykin, “Cognitive radio: brain-empowered wireless communications,” IEEE Journal on Selected Areas in Communications, vol. 23, no. 2, pp. 201-220, February 2005, herein incorporated in its entirety by reference, which he called it as multitaper-method singular-value-decomposition (MTM-SVD). In the MTM-SVD, the L cooperating CR users cooperatively estimate the interference temperature of the radio environment. As discussed in D. J. Thomson, “Spectrum estimation and harmonic analysis,” Proceedings of the IEEE, vol. 70, no. 9, pp. 1055-1096, 1982, herein incorporated in its entirety by reference, each cooperating CR applies mutitaper method to analyze the spectrum by first computing its kth eigenspectrum for the targeted band as:
                    Y                  k          ⁢                                                          (          l          )                    ⁡              (        f        )              =                  ∑                  n          =          1                N            ⁢                                    w            k                    ⁡                      (            n            )                          ⁢                              y            l                    ⁡                      (            n            )                          ⁢                  ⅇ                                    -              ⅈ                        ⁢                                                  ⁢            ω            ⁢                                                  ⁢            n                                ,      1    ≤    k    ≤    K  where yl(n) are the observed samples at the lth CR, and wk(n) represents the kth Slepian sequence (discussed in D. Slepian, “Prolate spheroidal wave functions, Fourier analysis and uncertainty,” Bell Syst. Tech. J., vol. 57, pp. 1371-1430, 1978, herein incorporated that each CR is to send its eigenspectrum vectorYl(f)=(Y1(l)(f),Y2(l)(f), . . . ,YK(l)(f)),1≦l≦L to the fusion center. Based on such vectors from each of the L cooperating CRs, the fusion center computes an L×K eigenspectrum matrix as:
      A    ⁡          (      f      )        =      [                                                      w              1                        ⁢                                          Y                1                                  (                  1                  )                                            ⁡                              (                f                )                                                                                        w              1                        ⁢                                          Y                2                                  (                  1                  )                                            ⁡                              (                f                )                                                              …                                                    w              1                        ⁢                                          Y                K                                  (                  1                  )                                            ⁡                              (                f                )                                                                                                    w              2                        ⁢                                          Y                1                                  (                  2                  )                                            ⁡                              (                f                )                                                                                        w              2                        ⁢                                          Y                2                                  (                  2                  )                                            ⁡                              (                f                )                                                              …                                                    w              2                        ⁢                                          Y                K                                  (                  2                  )                                            ⁡                              (                f                )                                                                          ⋮                          ⋮                          ⋱                          ⋮                                                                w              L                        ⁢                                          Y                1                                  (                  L                  )                                            ⁡                              (                f                )                                                                                        w              L                        ⁢                                          Y                2                                  (                  L                  )                                            ⁡                              (                f                )                                                                                                                                        w              M                        ⁢                                          Y                K                                  (                  L                  )                                            ⁡                              (                f                )                                                          ]  where wl are the weights of lth CR which is computed after taking into consideration the instantaneous environment information into account. Each row in A(f) corresponds to the eigenspectrum vector from a particular CR. If the primary user is present, the eigenspectrum vector consists of the PU signal plus noise. The noise is independent for the distributed CRs, while there will be a correlation in the PU signal part. Observing this fact, the MTM-SVD scheme exploits the correlation due to the PU signal by applying SVD to the eigenspectrum matrix 0:
      A    ⁡          (      f      )        =            ∑              k        =        1            K        ⁢                            σ          k                ⁡                  (          f          )                    ⁢                        u          k                ⁡                  (          f          )                    ⁢                        v          k          H                ⁡                  (          f          )                    where σk (f) is the kth singular value of A(f), uk(f) and νk (f) are the associated left and right singular vectors, respectively. Finally, the fusion center takes the spectrum occupancy decision based on the largest singular value of the matrix A(f). This method (MTM-SVD) provides a means for cooperative spectrum sensing to estimate the presence or absence of the primary user with high accuracy as discussed in J. Ma, G. Y. Li, and B. H. Juang, “Signal processing in cognitive radio,” Proceedings of the IEEE, vol. 97, no. 5, pp. 805-823, 2009, herein incorporated in its entirety by reference.
For the MTM-SVD scheme described above, the complexity of the whole procedure is quite high. Not only sending the K-dimensional vector from each CR to the fusion center would increase lots of communication burden over the reporting channel, but the SVD operation on the matrix A(f) is also computationally very expensive.
Eigenvalue based cooperative spectrum sensing has also been proposed in S. Xu, Y. Shang, and H. Wang, “Eigenvalues based spectrum sensing against untrusted users in cognitive radio networks,” in 2009 4th International Conference on Cognitive Radio Oriented Wireless Networks and Communications, 2009, pp. 1-6, herein incorporated in its entirety by reference. This method uses the eigenvalue based approach originally proposed in Y. Zeng, C. L. Koh, and Y.-C. Liang, “Maximum Eigenvalue Detection: Theory and Application,” in 2008 IEEE International Conference on Communications, 2008, pp. 4160-4164, herein incorporated in its entirety by reference. Observing the fact that the statistical covariance matrix of the observed signal will have different characteristics based on whether the PU is present or not, it has been proposed that an eigenvalue decomposition based approach. In this approach, the sample covariance matrix is computed from the observed signal's samples. Then the maximum eigenvalue (MEV) of the sample covariance matrix is calculated and the value is compared with a threshold to decide about the spectrum availability. This approach has been used in a cooperative fashion where each cooperating CR user performs the eigenvalue decomposition of the sample covariance matrix, and the MEV is computed. This MEV is compared with prefixed two-thresholds to decide about the reliability of the cooperating CRs. The CRs with reliable decision sends their decision to the fusion center, where the non-reliable ones send directly their MEVs to the fusion center. Finally, the fusion center fuses all the data to decide about the occupancy state of the spectrum. Although, the eigenvalue based spectrum sensing technique provides very good results without any prior knowledge about the channel, noise power, or PU signal, but the whole decomposition process is quite computationally expensive. Also the use of the random matrix theory to set the threshold values makes it difficult to obtain the accurate closed form expression for the thresholds.
Various soft-combination schemes with low-complexity have been discussed in J. Ma, G. Zhao, and Y. Li, “Soft Combination and Detection for Cooperative Spectrum Sensing in Cognitive Radio Networks,” IEEE Transactions on Wireless Communications, vol. 7, no. 11, pp. 4502-4507, November 2008, herein incorporated in its entirety by reference. In these schemes, each CR reports the value of the received energy to the fusion center, and the fusion center takes a decision based on a certain data-fusion (combining) criterion (or diversity combining) rule as discussed in A. Pandharipande and J.-P. M. G. Linnartz, “Performance Analysis of Primary User Detection in a Multiple Antenna Cognitive Radio,” in 2007 IEEE International Conference on Communications, 2007, pp. 6482-6486, herein incorporated in its entirety by reference. In D. Brennan, “Linear Diversity Combining Techniques,” Proceedings of the IRE, vol. 47, no. 6, pp. 1075-1102, June 195, herein incorporated in its entirety by reference, it was shown that, under the case of independent diversity branches, the optimum combining scheme is Maximal Ratio Combining (MRC). However, MRC requires full channel knowledge (amplitude and phase) for all branches. In MRC reception, the received signals {xl (t)}l=1L, where L is the number of diversity branches, are first co-phased, weighted proportionately to their channel gain and then summed up to yield a new signal xMRC(t)=Σl=1L hl*xl(t), where hl is the channel coefficient of the lth diversity branch. A less complex scheme is the traditional Equal Gain Combining (EGC), which doesn't require channel fading amplitudes estimation, and, under the case of identical and independent diversity branches, provides a comparable detection performance to that of MRC as discussed in S. P. Herath, N. Rajatheva, and C. Tellambura, “Energy Detection of Unknown Signals in Fading and Diversity Reception,” IEEE Transactions on Communications, vol. 59, no. 9, pp. 2443-2453, September 2011, herein incorporated in its entirety by reference, and A. Ghasemi and E. S. Sousa, “Opportunistic Spectrum Access in Fading Channels Through Collaborative Sensing,” Journal of Communications, vol. 2, no. 2, pp. 71-82, March 2007, herein incorporated in its entirety by reference. In EGC reception the received signals {xl(t)}l=1L, where L is the number of diversity branches, are co-phased only in each branch and then summed up to yield a new signal xEGC(t)=Σl−1Le−jφlxl(t), where φl is the phase of the lth diversity branch. Since the difference between MRC and EGC is not very large in terms of performance, but in terms of complexity, MRC is more complex than EGC, therefore we shall resort to EGC as our data-fusion rule and assume that a base station has the necessary information to perform EGC of received energy detector outputs.
FIG. 12 shows a flow chart of the soft decision time domain method 410 for a cooperative spectrum sensing network of CRs to determine whether a frequency band allocated to PUs is being used. The method includes a first step of calculating the energy in the frequency band 411, a second step of determining the received energy value 412, a third step of transmitting the CR result to a FC 413, a fourth step of the FC combining results from multiple CRs to obtain a final decision 422, and a final step of transmitting the final decision to the CRs 415.
FIG. 23 and FIG. 24 show simulation results for a network of ten CRs using the decision fusion (the OR rule and indicated in the figures by the diamond symbol) and using data fusion (EGC and indicated in the figures by the circle symbol). As discussed above, the performance degradation under fading environments can be mitigated by the use of multiples cooperating CR nodes. Below we will show the simulation results under additive white Gaussian noise (AWGN) and Rayleigh fading environments which shows the performance gain in combining ten cooperating CRs and using either data- or decision-fusion techniques. As discussed in A. Ghasemi and E. S. Sousa, “Opportunistic Spectrum Access in Fading Channels Through Collaborative Sensing,” Journal of Communications, vol. 2, no. 2, pp. 71-82, March 2007, herein incorporated by reference in its entirety, it has been shown that 10 cooperating users are sufficient enough to: 1) Provide high detection performance while keeping the probability of false-alarm extremely low, 2) Lower the required observation time and bandwidth, 3) Lower the required received SNR value, 4) Mitigate the fading effects.
The decision fusion (OR rule) approach requires fewer bits over the reporting channel (1-bit per user). On the other hand, when data fusion EGC is used, more feedback bits are required (m-bits per user, m≧1m≧1), which sacrifices the spectral efficiency. However, as shown in the simulation results above for cooperative spectrum sensing, data fusion outperforms decision fusion. Therefore, as can be seen from the above, we have a very clear tradeoff between performance and number of bits. One improvement of the hybrid data-decision method is that it minimizes communication bandwidth similar to data fusion while maintaining the performance of data fusion by employing a bi-threshold detector that switches between hard decisions (decision fusion) and soft decisions (data fusion) depending on the magnitude of the signal. When all CRs are equipped with bi-threshold detectors the network of CRs will self-select into a set of CRs with binary decisions and another set of CRs providing energy measurements, but not decisions, to the fusion center. Because many CRs provide decisions, requiring significantly less data be reported to the fusion center, the hybrid data-decision fusion method can substantially reduce the overall number of sensing bits over the reporting channel at the expense of a negligible loss in performance compared to EGC. Also, in contrast to the bi-threshold detector in C. Sun, W. Zhang, and K. Ben Letaief, “Cooperative Spectrum Sensing for Cognitive Radios under Bandwidth Constraints,” in 2007 IEEE Wireless Communications and Networking Conference, 2007, pp. 1-5, herein incorporated by reference in its entirety, which are used to perform only decision fusion, the hybrid data-decision fusion method exploits the information of those CRs sending soft decisions in order to improve the performance.